PyTorch equivalent to tf.nn.softmax_cross_entropy_with_logits and tf.nn.sigmoid_cross_entropy_with_logits

Question

I found the post here. Here, we try to find an equivalence of tf.nn.softmax_cross_entropy_with_logits in PyTorch. The answer is still confusing to me.

Here is the Tensorflow 2 code

import tensorflow as tf
import numpy as np

# here we assume 2 batch size with 5 classes

preds = np.array([[.4, 0, 0, 0.6, 0], [.8, 0, 0, 0.2, 0]])
labels = np.array([[0, 0, 0, 1.0, 0], [1.0, 0, 0, 0, 0]])


tf_preds = tf.convert_to_tensor(preds, dtype=tf.float32)
tf_labels = tf.convert_to_tensor(labels, dtype=tf.float32)

loss = tf.nn.softmax_cross_entropy_with_logits(logits=tf_preds, labels=tf_labels)

It give me the loss as

<tf.Tensor: shape=(2,), dtype=float32, numpy=array([1.2427604, 1.0636061], dtype=float32)>

Here is the PyTorch code

import torch
import numpy as np

preds = np.array([[.4, 0, 0, 0.6, 0], [.8, 0, 0, 0.2, 0]])
labels = np.array([[0, 0, 0, 1.0, 0], [1.0, 0, 0, 0, 0]])


torch_preds = torch.tensor(preds).float()
torch_labels = torch.tensor(labels).float()

loss = torch.nn.functional.cross_entropy(torch_preds, torch_labels)

However, it raises:

RuntimeError: 1D target tensor expected, multi-target not supported

It seems that the problem is still unsolved. How to implement tf.nn.softmax_cross_entropy_with_logits in PyTorch?

What about tf.nn.sigmoid_cross_entropy_with_logits?

Answer 1

- tf.nn.softmax_cross_entropy_with_logits

Edit: This is actually not equivalent to F.cross_entropy. The latter can only handle the single-class classification setting. Not the more general case of multi-class classification, whereby the label can be comprised of multiple classes. Indeed, F.cross_entropy takes a unique class id as target (per instance), not a probability distribution over classes as tf.nn.softmax_cross_entropy_with_logits can expect to receive.

>>> logits = torch.tensor([[4.0, 2.0, 1.0], [0.0, 5.0, 1.0]])
>>> labels = torch.tensor([[1.0, 0.0, 0.0], [0.0, 0.8, 0.2]])

In order to get the desired result apply a log-softmax to your logits then take the negative log-likelihood:

>>> -torch.sum(F.log_softmax(logits, dim=1) * labels, dim=1)
tensor([0.1698, 0.8247])

---

- tf.nn.sigmoid_cross_entropy_with_logits

For this one you can apply F.binary_cross_entropy_with_logits.

>>> F.binary_cross_entropy_with_logits(logits, labels, reduction='none')
tensor([[0.0181, 2.1269, 1.3133],
        [0.6931, 1.0067, 1.1133]])

It is equivalent to applying a sigmoid then the negative log-likelihood, considering each class as a binary classification task:

>>> labels*-torch.log(torch.sigmoid(logits)) + (1-labels)*-torch.log(1-torch.sigmoid(logits))
tensor([[0.0181, 2.1269, 1.3133],
        [0.6931, 1.0067, 1.1133]])

---

having imported torch.nn.functional as F.

Answer 2

The nn.CrossEntropyLoss outputs the same as tf.nn.softmax_cross_entropy_with_logits

>>> import torch

>>> loss_fct = torch.nn.CrossEntropyLoss(reduction='none')

>>> preds = np.array([[.4, 0, 0, 0.6, 0], [.8, 0, 0, 0.2, 0]])
>>> labels = np.array([[0, 0, 0, 1.0, 0], [1.0, 0, 0, 0, 0]])

>>> preds = torch.from_numpy(preds)
>>> labels = torch.from_numpy(labels)

>>> loss_fct(preds, labels)
tensor([1.2428, 1.0636], dtype=torch.float64)

The reduction param defaults to mean. I made it none to match your output.

nn.BCEWithLogitsLoss outputs the same as tf.nn.sigmoid_cross_entropy_with_logits

>>> tf.nn.sigmoid_cross_entropy_with_logits(logits=tf_preds, labels=tf_labels)
<tf.Tensor: shape=(2, 5), dtype=float32, numpy=
array([[0.91301525, 0.6931472 , 0.6931472 , 0.43748793, 0.6931472 ],
       [0.37110066, 0.6931472 , 0.6931472 , 0.79813886, 0.6931472 ]],
      dtype=float32)>

>>> loss_fct = torch.nn.BCEWithLogitsLoss(reduction='none')
>>> loss_fct(preds, labels, )
tensor([[0.9130, 0.6931, 0.6931, 0.4375, 0.6931],
        [0.3711, 0.6931, 0.6931, 0.7981, 0.6931]], dtype=torch.float64)